| Project/Area Number |
24540085
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kagoshima University |
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Principal Investigator |
YOKURA Shoji 鹿児島大学, 理工学研究科, 教授 (60182680)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAJIMA Kimio 鹿児島大学, 大学院理工学研究科, 教授 (40107850)
AIKOU Tadashi 鹿児島大学, 大学院理工学研究科, 教授 (00192831)
NAKAOKA Hiroyuki 鹿児島大学, 大学院理工学研究科, 准教授 (90568677)
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| Co-Investigator(Renkei-kenkyūsha) |
OHMOTO Toru 北海道大学, 大学院理学研究科, 教授 (20264400)
YASUDA Takehiko 大阪大学, 大学院理学研究科, 准教授 (30507166)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 特異多様体 / 相対Grothendieck群 / motivic 特性類 / algebraic cobordism / bivariant theory / fiberwise bordism group / Donaldson-Thomas不変量 / fiberwise bordism / motivic特性類 |
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| Outline of Final Research Achievements |
(1) We have constructed a bivariant-theoretic version of the natural transformation T_y_*:K_0(V/X) ->H_*(X, Q[y]) and Donaldson-Thomas type transformations of the natural transformation T_y_ * (the results were published in Advances in Mathematics and Journal of Singularities, respectivley). (2) We have considered the natural transformation T_y_ * on the symmetric product of spaces ( the results will be published in Crelles Journal (Journal fuer die reine und angewandte Mathematik)). (3) We constructed Oriented Bivariant Theory as a prototype of a bivariant theoretic version of Algebraic Cobordism of Levine-Morel-Pandharipande, and we introduced the notion of fiberwise bordism, motivated by or hinted by the method of constructing the Oriented Bivariant Theory and we constructed a bivariant analogue of the fiberwise bordism.
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